Espaces analytiques $p$-adiques au sens de Berkovich

Espaces analytiques

p

-adiques au sens de Berkovich

Ducros, Antoine

Séminaire Bourbaki : volume 2005/2006, exposés 952-966, Astérisque, no. 311 (2007), Exposé no. 958, pp. 137-176.

Résumé
Abstract

Il y a une quinzaine d’années, Berkovich a proposé une nouvelle approche de la géométrie analytique sur un corps ultramétrique complet. Elle fournit, contrairement aux précédentes, des espaces localement compacts et localement connexes par arcs. Elle s’est révélée particulièrement fructueuse pour l’étude d’une grande variété de questions ; citons par exemple les cycles évanescents ou quelques analogues $p$ -adiques de théories classiques : potentiel, dessins d’enfants, intégration le long d’un chemin, systèmes dynamiques...

Fifteen years ago, Berkovich suggested a new viewpoint on analytic geometry over a non-archimedean complete field ; the main difference between this viewpoint and the preceeding ones is that Berkovich’s spaces are locally compact and locally arcwise connected. This approach has been very fruitful ; for example it had applications to vanishing cycles, or to some $p$ -adic analogous of classical complex theories : potential, children's drawings, integration along a path, dynamical systems...

EuDML MR Zbl | 4 citations dans Numdam

Classification : 14G22, 14G20
Mot clés : géométrie analytique $p$-adique, géométrie rigide
Keywords: $p$-adic analytic geometry, rigid geometry

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     title = {Espaces analytiques $p$-adiques au sens de {Berkovich}},
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Ducros, Antoine. Espaces analytiques $p$-adiques au sens de Berkovich, dans Séminaire Bourbaki : volume 2005/2006, exposés 952-966, Astérisque, no. 311 (2007), Exposé no. 958, pp. 137-176. http://www.numdam.org/item/SB_2005-2006__48__137_0/

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